According to family tradition, the immigrant ancestor was Scots-Irish.

1) James Kinney/Kenny of Pennsylvania, father of Robert D. Kenny from the will
located at:http://www.pa-roots.org/data/read.php?896,386606,386606#msg-386606
James Kenny, farmer, late of MiddletonTownship, Cumberland County, PA;
will dated 7 September 1783; probated 28 July 1784.
Son Robert Kenny; daughter Elinor Kenny; to John Little,
husband to daughter Rachel; daughter Jane married to William McClurge.
Executors: Matthew Kenny and son Robert Kenny.
Witnesses: John Waddle, Brice Smith and Hugh Smith.
(Source: Cumberland County,
PA Wills; part of Book D, Books E
&amp; F; page 58)

2) Robert D. Kenny b. July 1, 1758, Lancaster Co. PA, d. Dec. 22,
1843, Haywood Co., TN.
Married 1783, Caroline Gryder, born 1763.
From the Membership Roster and Soldiers, The Tennessee Society of the Daughters
of the American Revolution 1894-1960:
Robert Kinney served as private in Militia of Lancaster County, Pa. He served
in Captain Alexander Martin's Company; Col. Peter Grubbs' Battalion of Militia
of Lancaster Co., Pa. (Vol. 7, P. 801, Pennsylvania Archives - Fifth Series.
He appears to have been given a "land grant" in TN for his service.
He and first wife, Caroline Gryder, moved there in
the early 1800s. He married second, Delila
Patton.† Because of her youth, it is
likely she was the mother of all listed Robertís children. Also note that her
father was named Thomas Patton and Robert named his second child Thomas P.
after the maternal grandfather.
Known children:
James, born Oct. 15, 1804, married Katherine Johnson
Thomas, born Sept. 12. 1813, married Ann SammonsGeorge W. Kinney b. abt.
1815 (see next generation)Penana, married Billy Pride
Rebecca, married Mr. Grimes
Robert D. Kennyís grave near son Thomas and George W farms:http://ftp.rootsweb.com/pub/usgenweb/tn/haywood/cemeteries/moore.txt

3) George W. Kinney b. abt. 1815, d. 1883 - of
Hardeman and Haywood counties, Tennessee.Married Lucinda J. Tucker.
All census data for George indicates he was born in TN. The 1880 census
indicates his father was born PA and his mother in TN.
George W. Kinney and his brother James changed
the original spelling from Kenny to Kinney for some reason. George and James
appear to have been very close as their children contain names of their
spouse.† Their brother Thomas kept the
original spelling and his subsequent descendents.
George W Kinney married under the Kenny name: http://ftp.rootsweb.com/pub/usgenweb/tn/hardeman/vitals/marriages/markaky.txt

4) John Wesley Kinney b. 14 Aug 1838, Haywood County, Tennessee, d.
16 Mar 1916, buried in Whiteville, TN.
Married Letitia F. Godwin/Goodwin.
John was in Mississippi
for about fifteen years and then returned to TN. In census data he is in his
father's household in TN through 1860, in Mississippi in 1870 and 1880, and in TN in
1900.
John W. Kinney cemetery location and information:http://ftp.rootsweb.com/pub/usgenweb/tn/hardeman/cemeteries/kinney.txt